# inverse Laplace transform

• Oct 1st 2009, 10:30 PM
ArTiCK
inverse Laplace transform
Hi all,

Using the s shifting theorem to find the inverse Laplace transform of:

F (s) = 3 / (s + 2)^2

I get the right answer but i am not sure if my working out is correct, would be appreciated if someone can tell me.

F(s +2) = L [e^(2t)* f(t)]

L[f(t)] = 3/ s^2

f(t) = L^(-1) [3/ s^2]
= 3t

g(t) = e^(2t) * f(t)
g(t) = 3t*e^(2t)

ArTiCk
• Oct 2nd 2009, 12:22 AM
mr fantastic
Quote:

Originally Posted by ArTiCK
Hi all,

Using the s shifting theorem to find the inverse Laplace transform of:

F (s) = 3 / (s + 2)^2

I get the right answer but i am not sure if my working out is correct, would be appreciated if someone can tell me.

F(s +2) = L [e^(2t)* f(t)]

L[f(t)] = 3/ s^2

f(t) = L^(-1) [3/ s^2]
= 3t

g(t) = e^(2t) * f(t) Mr F says: This should be $\displaystyle {\color{red}e^{-2t} \cdot f(t)}$. Note that F(s + 2) = F(s - [-2]) ....

g(t) = 3t*e^(2t) Mr F says: This should be $\displaystyle {\color{red}3t \cdot e^{-2t}}$